As a French, I don't really like the idea of having my country Balkanized...
Yet, since I know French History well, I know several scenario were France could have Balkanized.
A defeat and death of Philip Augustus at Bouvines seems too late in my opinion. Philip Augustus was an awesome king as he managed to make France from a Feudal Coalition to a somewhat unified Kingdom under the crown : you still had great lords such as the Dukes of Burgundy, the Counts of Flanders, or the Dukes of Britanny, but the French King had become stronger than them all. Plus, it's thanks to Philip Augustus the French heir to the crown did no longer require to be crowned during their father's lifetime. Thus, with the death of Philip II, the new king would still be Louis VIII.
Louis VIII was not an incompetent : while he ruled shortly (3 years, he died of dysentry during the Albegisian Crusade), he was a capable soldier and a good administrator. Plus, he was wedded to Blanche of Castille, who was his best advisor and quite competent. And the future Saint Louis IX was already born at that time, so strong Capetian Kings are still to come, and thus France is going to stay strong.
Also, I think you are overestimating John Lackland a bit. By the time of Bouvines, he had already fled back to England, having been scared at the Battle of the Roches-aux-Moines. In my opinion, the English Barons are probably already pissed off with him.
As for Otto IV, I don't think a victory at Bouvines would ease his situation. He was excommunicated, and he lead the attack at Bouvines... on a sunday! The day of the Lord! Philip Augustus could be seen to have fallen to Otto IV's treachery in that scenario, and the Pope isn't going to be happy : Christians were forbidden to fight on Sunday as it was the day of the Lord.
Now, if you want scenario where France get balkanized, here are a few ideas :
1) Have Louis III & Carloman II live longer and father sons to succeed them. While they co-ruled Western Francia (later France) together, Louis III was specifically charged with Neustria (Northern France) and Carloman II with Aquitaine and Burgundy (Southern France). Allowing them to live Longer and have sons could result on two French Kingdoms or more showing up.
2) Kill Robert II of France before the birth of one of his sons. Robert II was the only son of Hugh Capet, getting rid of him might get rid of the Capetians. Without Robert II, you have no clear successor to the throne and maybe an elective monarchy shows up, which could end dup leading to a somewhat HRE-esque France.
3) Have Philip II die before the birth of his son or be born as a girl. The succession in France would be quite unclear (Salic Law wasn't there before 1316, thus two hundread years later) at that point and there would be several candidates. These candidates would include :
-The count of Champagne Henri I, husband of Marie of France (first daughter of Louis VII), and after him his children.
-The count of Blois Theobald V, husband of Alix of France (second daughter of Louis VII), and after him his chidlren.
-Henry the Young King, husband of Margaret of France (third daughter of Louis VII).
-Richard the Lionheart, fianced to Alys of France (fourth daughter of Louis VII). He would require to be wedded to her of course.
-Count Robert of Dreux, younger brother to Louis VII (thus heir to the crown according to Salic Law) and his bloodline after him.